20 12 Neijiang senior high school entrance examination mathematics answer

This problem should be solved in a reciprocal way:

XY/X+Y= -2 can get x+y/xy =- 1/2, and it can be further changed into x/xy+y/xy =1/y+1/2.

Similarly YZ/Y+Z= 4/3, 1/y+ 1/z = 3/4 (2).

From XZ/X+Z= -4/3, we get 1/x+ 1/z =-3/4 (3).

( 1)+(2)+(3)

2×( 1/x+ 1/y+ 1/z)=﹣ 1/2

∴ 1/x+ 1/y+ 1/z=﹣ 1/4

The reciprocal of XYZ/(XY+YZ+XZ) is

xy+yz+xz/xyz= 1/x+ 1/y+ 1/z=﹣ 1/4

∴

XYZ / (XY+YZ+XZ)=﹣4

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